Oxford University Mathematician REACTS to "9 Math Riddles That'll Stump Even Your Smartest Friends"

Dr Tom Crawford - Mathematician at the University of Oxford and the University of Cambridge reacts to one of the most popular 'Math' videos on KZbin, with over 13 million views: "9 Math Riddles That'll Stump Even Your Smartest Friends".
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[@TomRocksMaths]

Watch the original video from Bright Side here: kzbin.info/www/bejne/qGazXplrlteDjqc

[@calebcheung7189]

Your video is very nicely done Better than theirs lol

[@KenFullman]

The last one (without the answer) is based on compression algorithms. The sequence is just saying what you see in the previous element. describing how many of each recurring digit So: 1 is just a single One ie One one (11) 11 is Two Ones. (21) 21 is One 2 followed by One one (1211) 1211 is One one followed by One two followed by two Ones (111221) 111221 is Three ones, followed by Two twos, followed by One one( 312211) So the next in the sequence would be 13112221 Simple

[@just.a.viewer]

u need pre-school 4 cheating :)

[@aidansmith4101]

@@KenFullman ha nice

[@infoyapper]

try solving IOQM exam from India

[@elijaholeary5139]

Waiiiiiiit whattt?! #5 says 50% divided by 2, not 50% divided by 1/2, they’re so gaslighting us!

[@Alo762]

This is not just annoying, its crazy! They _are_ wrong!

[@mlloser8318]

its 1/4 or 25% 50% is 1/2 and deviding it by 2 means 1/2 * 1/2

[@AtomicAndi]

95% of people don't understand percentages, so they easily get away with it. Almost fooled Tom as well ;-)

[@tristonlees6021]

I agree, the obvious answer is 25%. The given solution answers the question "Solve x/2 = 50%." Which *could* be read "What is 50% (when) divided by 2" but they ommit such clarifying words. Sure it isn't strictly necissary, but it's omition heavily implies another meaning. "Evaluate x = 50% / 2." The statement is deliberately subversive.

[@RoniSingh-m8m]

Xd how you messed up Question 2? 😅 ​@@mlloser8318

[@duet_1959]

A great example of "writing my 'riddles' ambiguously to make the reader feel like a donkey".

[@Wolb]

The last pattern is the “look and say sequence”, starting at 1… The number after 312211 is 13112221, because there’s 1 3, 1 1, 2 2, 2 1… but they didn’t ask for the next number, they asked for the *last* number in the sequence… The last digits will alternate between 11 and 21, so this sequence never ends, so there is no “last number”… unless you take 312211 as the last number they gave you…

[@thomashoglund5671]

Yes, I also recognized the John Conway sequence from the Numberphile video.

[@johnmcguiness3519]

@@thomashoglund5671 The Conway sequence is the look-and-say sequence starting with a 3, specifically, instead of a 1.

[@boblobgobstopper13214]

Thank you "please don't touch anything" for introducing me to this sequence

[@wasikancb]

So the correct answer would be 1? Because they didn't read the sequences as big numbers, but rather a sequence of one digit numbers without spaces. And the last number (digit) of the last sequence (of 1 digit numbers) of the infinite whole sequence, is 1 because it always is 1 and it can't be anything else than 1.

[@frankklemm1471]

But they not ask for the number (btw a Conway sequence), but "Can you figure out ...". So the answer must be "yes" when you can, otherwise "no" when you can't.

[@pichirisu]

That 50% question is legitimately incorrect. This is why language literacy is just as important as mathematics literacy when participating in doing math.

[@MegaOoga]

it was probably also incorrect on purpose to drive engagement in the comments

[@userkm2]

@@MegaOoga That is the problem. This gives birth to Terrance Howard's of the future

[@Smithers888]

Is there a rule of the internet that "there's an XKCD for that?" Because I entirely agree with what I think is Tom's main complaint and the same as Randall Monroe voiced 18 years ago in XKCD 169: "communicating badly and then acting smug when you're misunderstood is not cleverness."

[@Smithers888]

And for my less TL;DR commentary: #2: The order of operations "riddles" are so common online that this should be pretty easy. Note that it also highlights why BODMAS (or PEMDAS) doesn't even work: after M, you have 3+9-3+3; applying A next gives 12-6, which is 6. To get 12 you have to either use BODMSA or group as BO[DM][AS] or PE[MD][AS], applying addition and subtraction together. #3: I got "2, but they're going to tell me it's 3" because I think embedding maths notation implicitly groups that apart from the operations in the English text. At best, it's ambiguous (unlike #2, which is well-defined because it's all written in symbols). #5: The answer just straight-up lied about what the question was, so the video can *&^% right off with that one. #6: I see Tom missed the extra instruction "all you can use is addition" because it was spoken but not on the board. Which actually helps because the only thing you could use and then pretend is nothing is writing multiple 8s as one number. And then there's barely enough time to say "888 leaves 112, so plus 88 and plus however many are left as singles and I hope that works." #8: Tom's attempt imaginines extra '+' signs between the lines. I got to "do they want to ignore the first two lines and get 2 or join them into 1+1+1+1+11+1+1+1+11+1×0+1 = 30?" #9: The Look And Say Sequence is pretty instantly recognisable to sequence fans. Find it as OEIS A005150.

[@DrFunkman]

For #6, I did 8+8+8+8+8+8+8+8+936. They never said we have to ONLY use 8.

[@hughcaldwell1034]

I did (8 × 8 × 8) + (8 × 8 × 8) - (8 + 8 + 8), then realised I used nine 8s. Degree in pure maths and I can't count to nine, apparently.

[@mattc3581]

@@hughcaldwell1034 ((8*8*8)-8)*((8+8)/8)-8

[@peterb5]

⁠@@hughcaldwell1034or hear either apparently, it says you can only use addition😂

[@Tahgtahv]

@@peterb5 The part about only using addition was the only way I got it quickly. You need 5 8's in the units column to make 0, carry 4. Then 2 more 8's in the tens column for 0, carry 2. Then 1 more 8 in the hundreds column for 0, carry 1.

[@hughcaldwell1034]

@@peterb5 Oh damn... Yeah, really glossed over that one... I'm used to encountering variations of this question with a pretty standard stipulation that the four basic operators are allowed. I was mostly watching for the commentary anyway, though, since these types of questions are usually irritatingly trivial or just badly phrased.

[@paulooliveira4818]

I'm pretty sure the answer for #8 is a vector (5 5 2) since there are no symbols uniting the lines

[@general_isaac]

I originally got 12, and then quickly changed my answer to 30 after I saw they had omitted the missing plus signs on the end of each line. I thought they maybe wanted you to concatenate them to make two 11s, but apparently not 😂

[@adayah2933]

But you have no = signs after the first two lines, so clearly you are not supposed to give an answer to these.

[@ErikLeppen]

I do agree with Toms statement that riddles like these abuse math to wrongly make people think math is hard, and that this is a bad thing.

[@McJaews]

I really dislike these as a concept. Not the riddles themselves, but the whole "thing" around the riddles. The poorly written prompts, grammatical errors, taunting phrasing. Everything about these riddles feels like they're designed to prey on people who are easily influenced. They fish for engagement with every single aspect of their presentation.

[@msclrhd]

For problem #2 the same applies in programming. Programing languages have well-defined operator precedence rules which define the order of the operations, however adding parenthesis/brackets around the groups makes it easier to read/follow, especially for complex equations or logic checks.

[@GeekRedux]

18:16 Well, on that one, they aren't very clearly part of the equation. There are not math operators linking the first two lines to the last. The answer I got was a 5, another 5, and a 2.

[@weirdlyspecific302]

You're missing the point. Due to the lack of rigor in all of the previous problems, you simply can't determine what the person who created the problem intends, because anything is acceptable if it leads to more people getting the answer wrong.

[@tamirhammel5251]

I understood it as the last one from one line and the first line from the next line as 11, so the answer as 30

[@GeekRedux]

@@weirdlyspecific302 What the person intends is not relevant to my comment. Tom says the numbers are "very clearly part of the equation" and I'm saying that, because of the very lack of rigor you refer to, they are *not* _very clearly_ part of the equation.

[@nickgriffiths2796]

The last question - key is to read the numbers aloud to get the next number - the first number is one one - 11 (which is second number) - so the third number is two ones or 21 - which is one two then one one etc

[@youngms7971]

you’re a fucking genius my friend. bes wishes buddy you going far for real

[@bobrong9645]

Last one was especially non-math, the answer is 13112221: the previous number has one 3, followed by one 1...

[@maxv7323]

There is actually a fairly interesting bit of mathematics related to the "look-and-say" sequence. John Conway showed that the ratio between adjacent terms approaches a constant, and gave a polynomial with integer coefficients, of which said constant is a root.

[@remischmitt9308]

The sequence ends in a repeat: the same number will start appearing because it describes itself

[@maxv7323]

@@remischmitt9308 This is not true. The sequence grows (asymptotically) exponentially forever. The only starting number which results in a sequence that doesn't grow infinitely is 22, since that stays at 22.

[@GaborRevesz_kittenhuffer]

​@@remischmitt9308it's provably nonrepeating in the strict sense, i.e. it's nonperiodic. sure you'll see the same patterns reappear, but they will forever do so somewhat randomly.

[@BerndSchnabl]

#2 is just hilarious ..... you did it on purpose to make us feel better 😂 #5 is definitely wrong in the video and your answer was right. The question is "50% divided by 2" and the answer is "1/2 divided by 1/2"

[@gumpy4960]

So this is basically just ‘what am I thinking’ making you feel stupid when you can’t answer their stupidly worded questions.

[@yehet8725]

I've seen #8 multiple times online, and there they say that since there is no + in between the 1 at the end and the beginning of a row, its 11. So you basically add 4 + 11 + 3 + 11 + 0 + 1 = 30. But yeah.

[@smylesg]

That's what I got.

[@Tahgtahv]

You can't just ignore the carriage return. How does that in any way make sense? It's clearly 3 unrelated lines, specifically 2 expressions, and 1 equation that you need to finish.

[@adayah2933]

#3 they clearly got wrong too. In mathematical writing it is completely standard that a formula surrounded by text is treated as a whole. You never have a part of the formula interact with the text, and then with the rest of the formula. So the answer is unequivocally 2.

[@general_isaac]

There is something so pleasing about seeing a maths professor get as frustrated with these videos as me! 😂 I also made the exact same mistake as you on #6…

[@olivarra1]

I guess this just proves that most of the content on youtube is trash clickbait :'D Glad we have a few quality content creators!

[@davidhitchen5369]

"This golden rule of math always works." Terrance Howard doesn't agree.

[@Rodhern]

When I first noticed these 'order of operation' type riddle short videos, they were almost always about fighting over notation; as if there somehow was ONE correct interpretation. Often the parties arguing genuinely did not know better, as they had their particular 'correct' notation drilled into them at school over and over again (and had eventually given up resisting). Now we have math professors join in and tell what we (the non-resigned) knew all along: The notation means what we agree the notation means, and if there is doubt we should really agree ahead of time. So, rejoice, math fans, we won! (thank you Tom).

[@peterbrockway5990]

The thing about any expression is that it is attempting to express something. So the correct answer to "3+3x3-3+3" and its friends is always "Express yourself more clearly!"

[@Rodhern]

​@@peterbrockway5990 I find that often there is some context present, like a particular computer language or a particular math model problem, that will make the expression fairly well-defined (I guess 'fairly well-defined' is an oxymoron). The 'fun' or 'riddle' part is to some extent that the context is removed. Would it help if I go, say, "(3 + (3x3) - 3) + 3"? I am happy to go along with "3+3x3-3+3" when I feel I know the context. Are you more stringent, to the point, where you would still go "express yourself more clearly" even if you think you might be able to guess from the context? To me the win in this video is that WHEN the context might not be clear, or maybe entirely missing, THEN the expression defaults to largely undefined (or "bad notation" in Tom's words).

[@kylemauseth7579]

Brightside came up on my feed and was blocked after watching a video. I appreciate you doing this. Their videos are crap.

[@andrewjknott]

for 1+1+1+1+1 question, there is no operation between the lines (no hanging +), so they are different independent statements and have no bearing on the last statement. The last question is a description of the digits in the previous number in the sequence. 1 is described as "a single one" aka "one one" aka 11. 11 is described as "two ones" aka 21, then "one two, one one" aka 1211, etc... Numberphile did a video on it.

[@gitosalvador]

I didn't see any comments on puzzle #8 but the first 2 lines are not part of the equation because they don't have a plus sign in the end. Completely legit, very subtle trick.

[@jonathanbrewer7072]

Tom , do we have Oxford university mathematical papers from previous decades, centuries ??

[@shawngreen9794]

The 1+1+1… turned out to be 30… the lines wrapped around and there were two elevens in the middle of the list. One of the 1’s was multiplied by 0 so it disappeared. If I subtotaled, it would look like 4+11+3+11+1.

[@malcellery1538]

Thanks Tom, these daft problems seem to pop up more and more regularly.

[@geoffsmith1479]

The original video being reacted to should have been called "How to make a mathematician salty in nine easy steps"

[@haiphuc8049]

17:55 you could get another answer Those 2 1 can become 11 So it could be 30 as an answer

[@dyvel]

50% divided by 2 can't be 1, since they never say that it's 50% of 1. So since it's not 50% of anything specific, but 50% in general, the answer is 25% of that thing that we don't know of. If we were to accept that it's 1/2, we get 1/2 divided by 2, which is 1/2*1/2 = 1/4 Also, it's not 1/2/2, but rather

[@thedogatemyhomework8]

This isn't a math riddle video, it's just a "let's see if we can phrase it in a way that will make people make a mistake" type video. Fuck this, it's not about checking your math skills, it's checking whether you are following their stupid exact phrasing to the latter to find out the crooked answer their mind concocted.

[@emad3241]

50% divided by 2 is 25%, the author need to watch his own videos lol

[@kennethvalbjoern]

I'm MSc math and do not always respond correctly to riddles, even though I've constructed some crazy (correct) proof's over the years. Now I feel better.

[@Molurus73]

"Oxford University Mathematician doesn't now math operator precedence" is the headline here. What??

[@AndreiRotaru-m8h]

For #8, I was taught at school that if you have to change lines in an equation you need to say what are you doing next and follow it to the next line. Like in this case: 1+1+1+1+1+ +1+1+1+1+1+ +1+1x0+1 If it would be written like this then 12 is the correct answer. At least from what I was taught

[@ErikLeppen]

That would double the plus signs. Now for plus signs this doesn't pose problems, but it would if you do this with minus signs. 4- -2 is actually 6, because it says 4 - -2. If you continue a line, just write the operator at the end of the first line: 1+1+1+1+1+ 1+1+1+1+1+ 1+1*0+1 or, preferably, at the start of the next line: 1+1+1+1+1 +1+1+1+1+1 +1+1*0+1 The last is prefered because here too, if the line were broken at a subtraction, then the minus sign would be close to the subtracted number.

[@johng.1703]

hmm 50% divded by 2, so that would be 1/2 over 2/1 so that goes to 1/2 * 1/2 = 1/4.

[@MrMMochizuki]

I hate these too. It's just a bunch of semantic trickery. But they get it wrong. 50% divided by 2... then they say it's 1/2 divided by 1/2 = 1. That wasn't the original wording. They are just making shit up.

[@robmiller2811]

In fairness the 1+1+1+1+1 Has no continuing operation after the fifth one on the first line or the second line

[@scragar]

RE: order of operations The order we have exists because algebra is easier to do if you don't need brackets everywhere to make it clear 3X+5 means (3×X)+5 rather than the unintuitive 3×(X+5). Their teaching as a rule to kids who don't understand the reasoning is IMO part of the problem with the whole education there. No one writes such problems with numbers for anyone over 8 or 9 because by that time you're getting introduced to the basics of algebra and it stops being an issue.

[@VincenzoBarbato]

you have to count the number of digits: 1 11 21 1211 111221 312211 (3 ones, 2 twos, 2 ones)

[@KiraPepper]

I feel like too many students are not taught math in context. So BODMAS is what they are taught, when math is not in conext. When math is in conext (aka algeba etc) then students understand that all of their data (letters) needs to have a representation that makes sense. From the source to the product.

[@4iden.r]

😂😂😂 your reaction to them having an error in the video was so funny

[@jonathanbrewer7072]

Thank you, Tom. In its own way fascinating.

[@cchimozmin]

That’s John Conways see and say sequence. Count the number of each different digit and say it for the next number in the sequence

[@richardfarrer5616]

Firstly, I agree original video was painful but I don't feel Tom always came out well either. # 2 - no excuse. # 3 was ambiguous. The written question has an answer of 3 but the spoken question was more subtle. It was read as "What is half of (short silent pause} 2 + 2?" Linguistically, that is done to clarify meaning, just like brackets. Compare the question as spoken with "What is half of 2 (short silent pause} + 2?". The first form has an answer of 2; the second has an answer of 3. #6. Using just addition it's impossible. You need concatenation as well. But, allowing for that you can just use a greedy algorithm to guess the answer. You have to start with 888 to get close etc. #8. First two lines are not part of the equation since there aren't + signs at the end. Now, if you argued that the end of the first line and the beginning of the second were concatenated to give 11 (particularly after #6) then that would be legit. #9 OEIS A005150, the look-and-say sequence.

[@charlesc6011]

Q4: what is 40 divided by 1 divided by 2 plus 15. following order of operations; 40/1 = 40, 40/2 = 20, 20 + 15 = 35

[@paul454]

In the next to the last one, what's the operator between the first and second rows, and the second and third rows? There isn't one, hence they aren't part of the equation... I agree with your sentiments though. I really dislike "math" problems like these.

[@hauntedmasc]

I dunno mate, I think the one with the addition of 1's wasn't unfair, really. They definitely weren't connected by any operators to the last line... I got what they were going for at least, but I certainly sympathize with your distaste for it! The last one was a 'look and say' sequence, so '1' -> "one one" -> '11' -> "two ones" -> '21' -> " one two, one one" -> 1211 -> ...., so the next terms in the sequence would be 13112221, 1113213211, 31131211131221, 13211311123113112211, and so on, but again, unless you're familiar with it--and even they weren't, evidently, unless they were just driving engagement by "pretending" not to know--there's no reason to recognize it quickly.

[@maxv7323]

I interpreted the line breaks in the 1+1+1... to indicate concatenation, which I feel is a reasonable idea.

[@lucasdasilva23]

​@@maxv7323 me too, I guessed 552

[@nmklpkjlftmch]

You could argue that the blackboard for the addition of the 1s was simply too narrow and has some unfortunately placed line breaks, right in the middle of two elevens. Removing the line breaks gives 1+1+1+1+11+1+1+1+11+1x0+1 = 30

[@patrikskovalovs5692]

7th riddle is actually very easy ,because they're asking a yes or no question, and based on the previous riddles what they mean is how do you do it, but that is not what they wrote. and by that logic you can with good confidence just answer yes without even knowing if its right or not.

[@maysen1320]

the one with all the ones is definitely 2 after looking back because at the end and beginning of each line there is no function so they can't be a apart of the same equation

[@davidcawthorne7115]

50 percent divided by two is (1/2)/2 which is 1/4 or 25 per cent like you said.

[@newtoth85]

I think: "what is 50% divided by 2" is a tricky (and maybe poor) rewording of "what is divided by 2 ... 50%" So ONE is 50% WHEN divided by 2. Not explained well though.

[@Istillhaventgotanameforthis]

Doctor Thomas Crawford doesn’t know BIDMAS!

[@GrandRezero]

10 is the "say what you see" sequence. 1 is one 1. (11) i see two 1s.. (21) i see one 2 and one 1 (1211) the answer is 13112221

[@derekschreiber4844]

I was able to do #6 in the allotted time, but only since I had some experience with these videos and know some of the patterns in their answers. I also had to use some weird tricks to find the answer quickly. First I asked, “how could adding 8’s give us a 0 in the one’s place?” The only reasonable answer is by adding 8 five times, which would give us 40. I could then use similar logic to set the other digits to 0. I thought “how many times do I need to add 8 to the tens place to turn the 4 in 40 into a 0?” Well, twice because 8 + 8 + 4 = 20, so 80 + 80 + 40 = 200. Lastly, the hundreds place needed one 8 added to the 2 from 200 to set the digit to 0. 8 + 2 = 10, so 800 + 200 = 1000. Then, to get rid of the zeros in our numbers, we replace them with other 8’s. So long as we add one 8 in the hundreds place, 2 in the tens, and one in the ones place, we’ll get 1000. That’s how we get 888 + 88 + 8 + 8 + 8 = 1000.

[@johnchessant3012]

got 6/9. the ones I got wrong were the "half of 2+2" one, "50% divided by 2" (which I agree with Tom - they've messed that one up), and the "haha you're stupid, the first two lines weren't part of the equation" one (which is extremely inane in my opinion). also, what was the point of giving that last riddle without the answer? I've seen it before, and it is a bit of a nice challenge to figure it out so I'll put it under "Read more": this is Conway's "look and say" sequence! to get the next number just spell out the previous one: from 1211, we have "one 1, one 2, two 1s". Conway proved that the sequence never contains any digit more than 3, and the ratio of successive terms approaches a constant, 1.303577..., which is an algebraic number with a minimal polynomial of degree 71

[@maxv7323]

I think in the "What is 50% divided by 2?" they meant for it to be interpreted as "what results in 50% when divided by 2" which gets the "right" answer, but is obviously a nonsense interpretation

[@maysen1320]

he was right about the last problem if you say each number individually it reads the previous problem which I think when he said counting should be right

[@stephen2876]

Is it half of 2... plus 2 (three). But I clearly heard "What is half... of 2+2" (two). These kind of interpretive questions are REALLY maddening because both answers can be correct depending on how you ask the question.

[@davethesid8960]

The first two lines aren't connected to the third with any operation, they aren't even connected to each other.

[@peterkwan1448]

For #6, there is another more likely to be a math solution. [(8 + 8) * 8 - (8 + 8 + 8) / 8] * 8 = 1000 8 + 8 = 16 16 * 8 = 128 (8 + 8 + 8)/8 = 3 * 8 / 8 = 3 128 - 3 = 125 125 * 8 = 1000 For #9, the "last number" is ambiguous. The sequence can continue forever, so you cannot say that a number is the last number, in mathematical sense.

[@rmsgrey]

I have mixed feelings about BODMAS/PEMDAS/etc. Firstly, the acronym is imperfect because you don't do each letter in turn; you do brackets/parentheses first, then orders/indices/exponents/powers (and roots), then you do multiplication and division in the same pass rather then one before the other, then you do addition and subtraction in the final pass. To be consistent, it should be either BORMDAS or BOMA (or any of the many possible variants by changing which letter you pick for each entry). On the other hand, it does allow for a more compact notation - and the essential feature of most mathematical notation is that it allows you to express mathematical concepts with a minimum of ink - it's why we use single letters in algebra rather than "the unknown" or "the first unknown", why we use numbers rather than words to represent quantities, why we use symbols for operations, etc. On the gripping hand, while it's taken from a common mathematical notational convention used when writing polynomials (and similar expressions) - for example: x^2-4*x+3 relies on grouping the terms by doing the multiplication before the addition and subtraction - extending the convention to basic arithmetic and teaching it as a hard rule rather than a common convention gives it more weight than it's properly due. I also have some thoughts about specific questions: Question 3 (half of 2 + 2) was asked as two different questions. The written question could defensibly be interpreted as meaning "(half of 2) + 2", though both the positioning of the line break and the transition from words to notation suggest that the "2+2" is a single atomic expression embedded in the larger sentence rather than something divisible into its component notations. The spoken question, however, was unambiguously "half of (2+2)", with the pause after the half rather than after the first 2 - a nuance lost in the written notation, but which should be properly observed when speaking. I fully agree that question 5 (50% divided by 2) asked a different question than the one the video answered. For question 6 (make 1000 with eight 8s), I did answer correctly in the time given, but I'm familiar with questions about using n of a given digit and a limited set of operators to make a given total or range of totals, so I had concatenation in mind automatically. 1000/8 is 125, so you want 800, 80, 80, 8, 8, 8, 8 and 8, which becomes 888, 88, 8, 8 and 8. Incidentally, multi-digit numbers are another problem with BODMAS (etc) - concatenation of digits takes priority over everything, but isn't included in the acronym so if you just apply BODMAS to the string 12*3, you get the string 16, which is almost never going to be the intended answer. Question 7 (take one away from nineteen to give twenty) did get me - it's the only one where I didn't get the "right" answer and agreed that the "right" answer was right. On the other hand, I also agree with Tom that their answer was written wrongly. For question 8 (1+1+1+1+1 1+1+1+1+1 1+0*1+1=), I spotted the trick from the video's thumbnail, though I agree that the answer is not 2, but either "5 5 2" or "1+1+1+1+1 1+1+1+1+1 2" since the earlier lines do still exist in the question, so should be accounted for in the answer. Question 9 sets out the first few terms of the look-and-say sequence starting with 1, which has no last term since it continues growing indefinitely. The simple rule for generating the sequence is to transform each term into the next by reading from left to right, replacing each block of the same digit with 2 digits, the first being the length of the block; the second which digit was repeated. The operation is reversible (and may be easier to understand that way) - to get the previous term, simply break the term into pairs of digits, and replace each pair with the second digit of that pair repeated a number of times equal to the first of that pair, so 42 would become 2222 (which would become 2222 again, showing that the reversed operation is not, itself, reversible). So I give myself 8/9, and the video itself 7/9.

[@gavintillman1884]

As you say, some of those Qs are dire. 9 is quite interesting. Next time you are in Cambridge, try and find a back issue of the Archimedeans’ newsletter Eureka from maybe 1984, 85, somewhere round then. The issue you want has a yellow cover with cavemen on. Prof John Conway wrote an article on what he called “The Weird and Wonderful Chemistry of Audioactive Decay” aka the look and say sequence, which is the sequence in Q9. I see other comments have explained what it is so I won’t repeat that.

[@GaborRevesz_kittenhuffer]

the last one is actually a clever sequence i'd gotten acquainted with decades ago. i call it the "whatchu got?" sequence ...or the "read it back to me" sequence. it goes like this: start with 1: 1 "ok, whatchu got?" "i got one 1." 11 "whatchu got now?" "two 1s." 21 "now whatchu got?" "one 2, one 1." 1211 [...] "one 1, one 2, two 1s." 111221 312211 13112221 1113213211 . . . it has i don't know its oeis#, but it has a fancy name. last i checked it had no explicit formula, but many papers have been written about it, several standing/unresolved/unproven conjectures. it resembles a fractal... a 1-d aperiodic tiling...

[@GaborRevesz_kittenhuffer]

does anyone know if a 4 (or anything other than 1, 2 &3) will eventually crop up?

[@suranjans]

Tom, in the question adding a lot of ones (#8) there are no operators at the end (or start) of the lines, so that answer is 2. The bright side video is daft anyway.

[@jakekelly2436]

This was hilarious, thanks Tom 👍

[@Sam_on_YouTube]

Roman numberals took me a little longer than 15 seconds. More like 30. But I got all the others except the one that was just clearly wrong. For the one with 3 rows, I answered 5, 5, 2. It was clear that there was no operation between the lines. I'm counting that as correct. Though, really, a better answer would have been 1+1+1+1+11+1+1+1+11+1x0+1=30 But I think that says more about how many times I've seen these kinds of riddles. The only one I've seen on a good math channel was the last one. It's a look and say sequence. They've been on numberfile a few times. The answer is 13112221 because the last number has one 3, then two 2s, then two 1s.

[@diegorosa7517]

#5 Definitly wrong. 50% is being divided by 2 and not by half

[@x-x]

You've got #1, #3, #4, #5 (Bright Side was wrong in #5) right and #2, #6, #7, #8 wrong. In my opinion you've got #7 and #8 perfectly right, their answer is really stupid in these cases. #9 has no answer, I saw it once on Reddit and there's a funky function for that, other than that it may be literally anything, like number of letters or Roman Numerals or just about anything imaginable, not even remotely connected to maths.

[@hypermagellan]

There was a function for that last one!?!!?! Thats incredible... what was that function?

[@hypermagellan]

My math teacher actually showed that last riddle for us. The answer (not math related): 13112221 Explanation: 1st number: 1 2nd number: 1 = "one one" = 11 3rd number: 11 = "two one" = 21 4th number: 21 = "one two one one" = 1211 5th number: 1211 = "one one one two two one" = 111221 6th number: 111221 = "three one two two one one" = 312211 7th number: 312211 = "one three one one two two two one" = 13112221

[@gamatorking3549]

Who called you a mathematician if you can't remember bodmas ( a 5th standard concept)

[@gtziavelis]

The way that the sensationalist narrator throws in value judgments like "pull yourself together because the next one is coming", haha, they know full well that they are anti-educational! This much is not up for debate. And TomRocksMaths is one of the best educational KZbin channels. Thank you Tom. I got the 13112221 on their last question but it was a trolly one for sure.

[@eidodk]

The way they are written on the board, they are clearly NOT part of the equation. There's no operator after the numbers or equal signs in the first two lines - The last one is: The next number in the line is 13112221 ... The sequence is the number of numbers in the last number.

[@andrewkepert923]

#5: 50 percent divided by 2 = 50, per (cent / 2) = 50 / (100/2) = 1. Or something like that. 🫤

[@fabriziogalli88]

For me it was quite simply 8000/8 + 8 - 8 + 8 - 8 + 8 - 8

[@ikocheratcr]

This "bright side" video sounds more like click bait that anything else. The most insulting one is the last one. All "questions" tricky or ambiguous.

[@klausao]

First, it is AI voice, second, the board is green and not black. Zero is not a number,,,. But you are funny, great work!!!

[@marklondon9004]

This video makes me want to encourage my son to become a first year with you one day.

[@HeidiBullard]

I really like watching you do maths. I found you through your reactions to Alan Becker and stuck around to watch you be a nerd, lol. I really dislike these type of riddle math videos because they all seem to fit the answer to how stupid/frustrated the video creator wants people to feel.

[@michaelsun-qh5xe]

Hi Tom, it would be wonderful to see you attempting the hsc ext 2 math exam of 2023, or 2022, you took standard last time want to see you do this once before I go on to take the 2024 version love from AUS

[@vixguy]

18:00 the answer is actually 30! Notice how the second and third row end and start with a 1 respectively. same thing with first and second row

[@pauldekker3119]

with you on all your comments.

[@Derply]

for the 1+1+1+1+1 one where it wasnt part of the equation, i feel a "better" answer would be that the numbers on the end and start make 11 as there are no +s between, but it feels like a badly made question

[@okaro6595]

3:45 That is easy: 3 x 3 = 9, then the 3 and -3 cancel and you just add the last 3. Order of operations is easy if you understand the reason. If you buy 3 bananas each $2 and 5 apples each $5 it costs 3*2 + 5*5. Students seldom are told the reason. They are just told the rule and some acronym to remember it. I think the #3 was wrong. Arithmetic formulas take precedence over words. In the #5 they clearly made an error. They said divided by 2, but then divided by 1/2, likely mixing with the previous one.

[@shayanchamas60]

These questions are just plain stupid. They're not maths, instead they are like those matchstick puzzles.

[@aidansmith4101]

6:00 when i was a wee little lad in school they taught me PEMDAS or BEMDAS (their quite similar) parenthesis exponents multiplication division addition subtraction.

[@aidansmith4101]

love how number three frogets proper grammar tho

[@hackjokes9901]

#3 simply because there are no brackets

[@Syntax753]

Multiplication precedes addition - I wouldn't call it stupid or that it's using bad notation. It's critical for software development, and I'm a bit surprised by your reaction TBF

[@DarinBrownSJDCMath]

Funny how #9 is the only one with any real mathematical interest. It's sequence A005150 at OEIS.

[@adayah2933]

I don't think there is any mathematical interest in that sequence. OEIS contains literally everything, mostly garbage.

[@DarinBrownSJDCMath]

@@adayah2933 Really? Can you tell me the 71st degree polynomial whose unique positive root is the limiting ratio of the lengths of its consecutive terms? With a proof? I didn't say the sequence had immense, fundamental mathematical interest. I just said it had SOME mathematical interest. In comparison to the other "puzzles", which have none whatsoever.

[@mda99das]

the 8 eights question, (8*8*8)+(8*8*8) gives 512+512 = 1024. log 2 8 and multiply that by the remaining 8 is 3*8 = 24 . 1024-24 = 1000

[@gary.h.turner]

But the log 2 requires a 2, which isn't allowed (only 8s!), * (multiplication) isn't allowed, and the 1024-24 is a subtraction, which also isn't allowed (only addition can be used, if you listen to the original question).

[@DrWatson28]

First two lines don’t count made me laugh out loud lol

[@yamikira6512]

18:10 There is no operation sign between last "1" in a row and the first "1" in the next row. You assumed there is an addition

[@maxv7323]

I feel like your comment on the second problem is going a bit far in the war against bad order of operations problems. Usually these problems include a part where different commonly used standards for order of operations obtain different results, the most common being the idea that "implicit multiplication" (multiplication without a multiplication symbol) takes priority. The thing about "riddle" #2 in this video, is that all order of operations standards, at least out of the ones I've seen, evaluate it to the same number. Order of operations is arbitrary, yes, but it is still extremely useful in math communication as it can massively simplify expressions. Its a lot faster to write ax^2+bx+c than (a(x^2))+(bx)+c. Even outside of arithmetic, its faster to write and easier to read $ eg p \lor q$ rather than $( eg p) \lor q$. Also in the "what is 50% divided by 2?" they probably wanted it to be interpreted as "what when divided by 2 results in 50%" which gives the "right" answer but is obv a nonsense way to interpret it.

[@eidodk]

He was clearly embarrassed, because as soon as he got bamboozled about the most basic math, the entire video became a defense of his thinking.

[@msclrhd]

That "The Map of Mathematics" video by Domain of Science would be interesting to react to.

[@aidansmith4101]

on number 4 im confused because we arnt dividing by 1/2 we are dividing by 2...

[@mineln97]

not knowing PEMDAS as an Oxford teacher is quite embarrassing ngl

[@Metheglyn]

@mineln97 He knows PEMDAS. The version he was taught was BODMAS, which contains exactly the same information. PEDMAS is used in some communities, and is equally valid, since M and D has the same priority anyway.

[@AndreiRotaru-m8h]

In #5 I was thinking of: 50/100 / 2 = 1

[@InfiniteWithout]

I wonder if there is an equation where 1 2 and 3 are all correct answers

[@Alo762]

Answer to 9 is 13112221. One of digit 3, one of digit 1, two of digit 2 and 2 of digit 1. I have seen this earlier somewhere. I also hate this kind of "tests". At least when I am sober. [Just as some other also found out below.]

[@brianjrobinson]

I've long advocated that we should stop teaching order of operation and teach to write unambiguous equations instead.

[@JoePortly]

About thirty years ago there was an (Associated Examinations Board?) advanced-level English GCE that came with directions along the lines of 'Answer 4 questions in-all - 3 from section A and 2 from section B'. But the candidates didn't expect a mathematics test